【西南大学】[机考][1245]《几何学》复习题部分资料

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【西南大学】[机考][1245]《几何学》
试卷总分:100    得分:100
第1题,外积满足交换律
对
错
正确资料:


第2题,射影平面可使中心射影一一对应
对
错
正确资料:


第3题,共线向量一定是共面向量
对
错
正确资料:


第4题,混合积等于3向量为棱边的平行六面体的体积
对
错
正确资料:


资料来源：谋学网（www.mouxue.com）,平面既是柱面又是锥面
对
错
正确资料:


第6题,柱面不是二次曲面
对
错
正确资料:


第7题,射影点没有点方程
对
错
正确资料:


第8题,三点形的对偶图形就是它自己
对
错
正确资料:


第9题,二次锥面是旋转曲面
对
错
正确资料:


资料来源：谋学网（www.mouxue.com）,二次曲线的中心不可能是无穷远点
对
错
正确资料:


第11题,下列二次曲面属于直纹面的是（    ）
A.椭球面
B.单叶双曲面
C.双叶双曲面
D.双曲抛物面
正确资料:、D


资料来源：谋学网（www.mouxue.com）,两向量共线的充要条件是(     )
A.两向量线性相关
B.两向量的外积是零向量
C.两向量线性无关
D.有一向量是零向量
正确资料:、B


第13题,下列关于二次曲线奇异点的性质表述正确的是(       )
A.二次曲线无奇异点
B.二次曲线的奇异点可以有无穷多个
C.二次曲线的奇异点可以只有一个
D.奇异点一定在二次曲线上
正确资料:、C、D


第14题,下列命题表述正确的是(        )
A.不同心的两个射影对应线束，对应直线的交点全体一定是非退化的二次曲线
B.同心的两个射影对应线束，对应直线的交点全体一定是退化的二次曲线
C.不同心的成透视对应的两个线束，对应直线的交点全体一定是退化的二次曲线
D.同心的两个射影对应线束，对应直线的交点全体一定不是退化的二次曲线
正确资料:、C


资料来源：谋学网（www.mouxue.com）,下列关于二次曲线性质叙述正确的是(      )
A.二次曲线的中心的极线是无穷远直线
B.无穷远点关于二次曲线的极线是二次曲线的直径
C.彼此平分与对方平行弦的两直径是一对共轭直径
D.渐进线是直径，其共轭直径就是它本身
正确资料:、C、D


第16题,三向量共面的充要条件是(        )
A.三向量线性相关
B.有一个向量是零向量
C.一向量是另外两向量的线性组合
D.三向量混合积是零
正确资料:、C、D


第17题,关于点列和线束的命题叙述错误的是(        )
A.点列和线束之间不能建立射影对应
B.两不同点列之间透视对应就是两直线间的中心射影
C.两不同线束之间的透视对应是一一对应
D.透视对应是射影对应
正确资料:


第18题,点P(3,4,5）绕Oz轴旋转生成的圆的方程_____________
正确资料:</strong><br/><img width="136" height="23" class="kfformula" style="width: 136px; height: 23px;" src="data:image/png;base64,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" data-latex="{x}^{2}+{y}^{2}+{z}^{2}=50,z=5"/>               
                                                                                                                        <br/>


第19题,
正确资料:


资料来源：谋学网（www.mouxue.com）,已知交比(AB,CD)=1/2，则(AC,BD)=________
正确资料CA,BD)


第21题,
正确资料:


第22题,直线上参数分别为1，0，的三点分别对应0，，1的三点的射影变换参数表示是_________________
正确资料:</strong><br/><img width="106" height="25" class="kfformula" style="width: 106px; height: 25px;" src="data:image/png;base64,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" data-latex="\lambda {\lambda }^{&#39;}-\lambda +1=0"/>               
                                                                                                                        <br/>


第23题,
正确资料:


第24题,已知向量a=(1,1,0),b=(2,03),则________
正确资料:


资料来源：谋学网（www.mouxue.com）,
正确资料:


第26题,曲面与y-z=0的交线在xoy面上的射影曲线为_________
正确资料:</strong><br/>y-z=0,x=0<br/>               
                                                                                                                        <br/>


第27题,
正确资料:


第28题,通过原点与点(6,-3,2)且和平面4x-y+2z=0垂直的平面方程是________
正确资料:</strong><br/>2x+2y-3z=0<br/>               
                                                                                                                        <br/>


第29题,
正确资料:


资料来源：谋学网（www.mouxue.com）,向量a=(1,1,0),b=(1,0,1)的夹角是_______
正确资料:</strong><br/><img class="kfformula" src="data:image/png;base64,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" data-latex="\frac {\pi } {3}"/>               
                                                                                                                        <br/>


第31题,
正确资料:


第32题,求由两个自对应点1，2所确定的对合方程
正确资料:求由两个自对应点1，2所确定的对合方程


第33题,
正确资料:


第34题,求过点(1,0,-2)且和两直线与都垂直的直线方程
正确资料:


第35题,
正确资料:


第36题,已知两条直线m: 和n:,证明m和n是异面直线。
正确资料:


第37题,
正确资料:


第38题,已知二次曲线,(1)证明它是双曲线；(2)求中心坐标；(3)求与直线平行的直径及其共轭直径的方程；(4)求渐近线方程
正确资料:</strong><br/><img style="vertical-align: middle; margin-right: 2px;" src="/ueditor/dialogs/attachment/fileTypeImages/icon_doc.gif"/><a title="38解.docx" style="font-size:12px; color:#0066cc;" href="/resourcefile/uploadFiles/file/attachFiles2018/2019/03/11/201903111552308180521017109.docx">38解.docx</a></p><p><br/>               
                                                                                                                        <br/>


第39题,
正确资料:


第40题,设三点形ABC的边AB,BC,CA绕同一直线上三点P,Q,R旋转，顶点B,C在两条定直线上，求证:顶点A也在一条定直线上
正确资料:</strong><br/>证明：因为<img width="198" height="24" class="kfformula" style="width: 198px; height: 24px;" src="data:image/png;base64,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" data-latex="(B,{B}_{1},{B}_{2},\cdot \cdot \cdot )\to (C,{C}_{1},{C}_{2},\cdot \cdot \cdot )"/>,则<img width="216" height="21" class="kfformula" style="width: 216px; height: 21px;" src="data:image/png;base64,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" data-latex="(B,{B}_{1},{B}_{2},\cdot \cdot \cdot )\to R(C,{C}_{1},{C}_{2},\cdot \cdot \cdot )"/>在这两个射影线束中，PR是自对应直线，所以这两个线束是透视对应，对应直线的交点<img width="91" height="20" class="kfformula" style="width: 91px; height: 20px;" src="data:image/png;base64,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" data-latex="A,{A}_{1},{A}_{2},\cdot \cdot \cdot "/>共线               
                                                                                                                        <br/>


第41题,
正确资料:


第42题,如果3向量a,b,c不共面，那么,,也不共面
正确资料:</strong><br/>因为<img class="kfformula" src="data:image/png;base64,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" data-latex="(a\times b,b\times c,c\times a)=[(a\times b)\times (b\times c)]\cdot (c\times a)=(abc)b\cdot (c\times a)={(abc)}^{2}" width="519" height="27" style="width: 519px; height: 27px;"/>,而a,b,c不共面，所以<img class="kfformula" src="data:image/png;base64,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" data-latex="(abc)" width="54" height="26" style="width: 54px; height: 26px;"/>不等于0，因此</p><p><img class="kfformula" src="data:image/png;base64,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" data-latex="(a\times b,b\times c,c\times a)" width="155" height="24" style="width: 155px; height: 24px;"/>不等于0，从而三向量<img class="kfformula" src="data:image/png;base64,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" data-latex="a\times b,b\times c,c\times a" width="143" height="31" style="width: 143px; height: 31px;"/>不共面               
                                                                                                                        <br/>


第43题,
正确资料: